Geoffrey Mason

Recovery of oil by spontaneous imbibition

Spontaneous imbibition is of particular importance to oil recovery from fractured reservoirs. There has been a surge in the growth of technical literature over the past 5 years. This review is centered on developments in the scaling of laboratory imbibition data. Results for variation in interfacial tension, wetting and non-wetting phase viscosity, sample size, shape and boundary conditions, and initial wetting phase saturation have been correlated for a variety of strongly water-wet rocks as plots of normalized oil recovery vs. dimensionless time. Correlations have been tested for weakly water-wet conditions induced by adsorption from crude oil. In situ fluid saturation measurements have been used to distinguish between modes of imbibition that range from frontal to global displacement. Research on surfactant-enhanced imbibition has advanced from laboratory to field tests.

Capillary behavior of a perfectly wetting liquid in irregular triangular tubes

Abstract Triangles provide a useful example of simple pore shapes: they have angular corners, which can retain liquid, and irregular triangles give a wide range of shapes. The exact meniscus curvature of perfectly wetting liquids draining from pores of general triangular cross section is derived. The appropriate normalized shape factor for capillary action in triangular pores is the ratio of the area of cross section, A, to the square of the perimeter length, P. The drainage penetration curvature is calculated for all possible shapes of triangular tubes. The amount of wetting phase that drains at the penetration curvature decreases as aspect ratio increases. The remaining liquid is retained in the corners of the triangular pore. Thus, after drainage, there is dual occupancy of the pore and continuity of both wetting and nonwetting phases. The decrease in liquid retained in the corners with increase in curvature of are menisci subsequent to penetration is also calculated. The relation between saturation and the square of the curvature is shown to be hyperbolic. Imbibition occurs by the progressive filling of corners. At low saturations imbibition is the exact reverse of drainage. Corner filling continues even when the meniscus curvature falls below the drainage penetration curvature, thus giving hysteresis. When the menisci in the corners meet, the liquid spontaneously redistributes. A portion of the tube length refills and the meniscus curvature jumps to the drainage penetration curvature. Spontaneous redistribution is an example of “snap-off” and may give rise to the entrapment of nonwetting phase. Both the curvature and saturation at which spontaneous filling occurs are derived as a function of shape factor. The triangular pore has much greater versatility than the commonly used cylindrical pore, and models, in a simple way, several basic features of the capillary behavior of highly complex porous materials.

Effect of contact angle on drainage and imbibition in regular polygonal tubes

Abstract Wettability and pore structure are primary factors in determining the capillary behavior of porous media. A key characteristic of the pore structure of real porous media is the angular corners of the pores. As a model of pore structure, angular tubes are much more realistic than the commonly used cylindrical tube model. However, their behavior is quite complicated because contact angle, corner angle, and the meniscus in the corners are all variables. The Mayer and Stowe-Princen (MS-P) theory of drainage, together with a detailed model of meniscus behavior in a corner during imbibition, enables the relationships between capillary pressure and saturation to be investigated as a function of contact angle and pore geometry. In this study, a general relationship between contact angle, corner angle, liquid saturation, and the curvature of a meniscus in the corner of an n -sided tube is derived. For any corner angle, there is a critical contact angle at which the meniscus becomes flat and the capillary pressure falls to zero. Drainage of polygonal tubes (having cross-sections such as equilateral triangles and squares) is analyzed as a function of contact angle using the MS-P theory. For imbibition, there are two filling mechanisms: the tube can be filled by a meniscus advancing along the tube or it can be filled by expanding the menisci from the tube corners. For both mechanisms, the contact angle is treated as having either zero or finite contact angle hysteresis. Systematic changes in drainage and imbibition capillary pressure curves with contact angle are obtained. The results are qualitatively consistent with several features of the behavior of natural porous media, including the effect of wettability on the displacement efficiency of crude oil by water.

The effect of pore space connectivity on the hysteresis of capillary condensation in adsorption—desorption isotherms

Abstract A method of determining the connectivity of the pore space of an adsorbent from the hysteresis of the adsorption—desorption isotherm is proposed. The analysis depends upon being able to theoretically separate the amount adsorbed into capillary condensation and surface adsorption and uses the amount of capillary condensation on the adsorption isotherm at the relative vapor pressure of the desorption knee as the variable determining connectivity. As an example the analysis is applied to known isotherms for Linde silica.

Meniscus curvatures in capillaries of uniform cross-section

Menisci contained in capillaries of uniform cross-section can be broadly classed according to whether wedge-like liquid structures exist, as in triangular-section tubes, or do not exist, as in circular-section tubes. In tubes which form wedge menisci the liquid in the wedge adopts a form so that a section through the liquid surface is the arc of a circle. The volume of liquid per unit length of the wedge is constant along the tube. A non-wedging meniscus, however, is locally bounded by its tube and has a curvature inversely proportional to the hydraulic radius of the tube. Mayer and Stowe (J. Colloid Interface Sci., 1965, 20, 893) proposed an approximate method of determining the mean surface curvature of menisci in sphere packs. It was later applied independently by Princen (J. Colloid Interface Sci., 1969, 30, 60) to estimating capillary rise in spaces between parallel rods. The method, which incorporates the presence of wedges, is shown to be exact for determining mean surface curvatures in systems where the meniscus is undistorted by gravity. Experimental confirmation of the theoretical predictions to within 1.5% was obtained from measurements of capillary rise of a perfectly wetting liquid in tubes formed either by a rod and a square corner or by two rods and a plate. The conditions of pore geometry and contact angles which give rise to wedge menisci are discussed and illustrated by examples which include menisci in tubes of polygonal section.

Desaturation of porous media. I. Unconsolidated materials

Abstract A model of the pore space in a random packing of rotund particles is suggested. The assumption that the pores are randomly connected enables the residual number of undrained pores to be calculated, independent of pore size distribution. There are two distinct mechanisms by which liquid can leave a pore; 1. (i) by evaporation 2. (ii) by fluid flow Desaturation by fluid-flow without evaporation is considered in two ways: a) flow through the whole pore space; and b) a modification where flow also occurs through incipient pendular rings. The shape of the capillary pressure curve, normalized to a window size distribution, is given for each of these cases. The relative permeability to both wetting and nonwetting phases is given for monosized windows. The relative permeability for an idealized window size distribution during desorption is derived. An approximation to Archies Law is obtained. The analysis indicates deficiencies in both mercury porosimetry and desorption as methods for measuring “pore size distributions”. When applied to the random packing of equal spheres, for which an approximate window size distribution is already known, the theory gives a capillary pressure curve which is in reasonable agreement with experiment.

Bubble Snap-off and Capillary-Back Pressure during Counter-Current Spontaneous Imbibition into Model Pores

A previous paper (Unsal, E.; Mason, G.; Ruth, D. W.; Morrow, N. R. J. Colloid Interface Sci. 2007, 315, 200-209) reported experiments involving counter-current spontaneous imbibition into a model pore system consisting of a rod in an angled slot covered by a glass plate. Such an arrangement gives two tubes with different cross-sections (both size and shape) with an interconnection through the gap between the rod and the plate. In the previous experiments, the wetting phase advanced in the small tube and nonwetting phase retreated in the large tube. No bubbles were formed. In this paper, we study experimentally and theoretically the formation of bubbles at the open end of the large tube and their subsequent snap-off. Such bubbles reduce the capillary back pressure produced by the larger tube and can thus have an effect on the local rate of imbibition. In the model pore system, the rod was either in contact with the glass, forming two independent tubes, or the rod was spaced from the glass to allow cross-flow between the tubes. For small gaps, there were three distinct menisci. The one with the highest curvature was between the rod and the plate. The next most highly curved was in the smaller tube, and the least highly curved meniscus was in the large tube and this was the tube from which the bubbles developed. The pressure in the dead end of the system was recorded during imbibition. Once the bubble starts to form outside of the tube, the pressure drops rapidly and then steadies. After the bubble snaps off, the pressure rises to almost the initial value and stays essentially constant until the next bubble starts to form. After snap-off, the meniscus in the large tube appears to invade the large tube for some distance. The snap-off is the result of capillary instability; it takes place significantly inside the large tube with flow of wetting phase moving in the angular corners. As imbibition into the small tube progresses, the rate of imbibition decreases and the time taken for each bubble to form increases, slightly increasing the pressure at which snap-off occurs. The snap-off curvature is only about two-thirds of the curvature of a theoretical cylindrical meniscus within the large tube and about 40% of the curvature of the actual meniscus spanning the large tube.

Holdup and dispersion: tracer residence times, moments and inventory measurements

Abstract The inventory function is the quantity of tracer remaining in a continuous-flow system at elapsed time t when steady flow of the tracer is replaced by untraced flow at t = 0. The relations between residence-time distributions, moments and changes in inventory when a tracer is flushed from a system are established. It is shown that inventory measurements could be an attractive way of measuring moments. In particular, the mean residence time is given by the intercept on the baseline of the initial tangent to the inventory curve, and the variance by the area between the inventory curve, the initial tangent and the baseline. It is proposed that dispersion be defined in terms of the variance of the residence-time distribution. This would allow experimentalists to record their results independently of models or theories in addition to comparing their results with the predictions of theories. Methods based on inventory measurements are potentially more accurate than the traditional step- and pulse-response methods. Ways in which inventory measurements might be made are suggested. It is timely that the theory should be presented now because tomographic methods that could be used to measure inventory are starting to appear.

Capillary viscometry by perturbation of flow and composition

Abstract A new technique for making viscosity measurements on gas mixtures is introduced. The composition and flowrate of a mixture flowing through a capillary tube are perturbed by adding a small stream of perturbation gas. This is usually a pure, individual component of the mixture. The pressure at the inlet of the capillary tube rises when the perturbation gas is added and this pressure increase is proportional to the flowrate change. Because there is empty volume between the point where the perturbation gas is added and the capillary tube, it is some time later that the pressure changes again when the composition of the gas flowing through the tube changes. This second pressure change is proportional to the change in viscosity. The ratio of these two steps of pressure is proportional to d ln μ/dXi where μ is the viscosity and Xi is the mole fraction of component i. An apparatus has been developed which is capable of making measurements with suitable precision and some preliminary data for the nitrogen–argon system at 1.2 bar and 24°C are given.

Gas Adsorption Isotherms from Composition and Flow-Rate Transient Times in Chromatographic Columns II. Effect of Pressure Changes

In the previous paper a method was described for measuring binary adsorption isotherms by a chromatographic method. The method involved making simultaneous small perturbations to the concentration and flow-rate of the stream entering a packed column and observing the changes with time of the composition and flow-rate of the gas leaving the column. The perturbation to the inlet flow was made by adding a small extra stream of gas of known composition to the main flow passing through the columns. The present paper describes the effect of the increased mean pressure in the column caused by the small increase in flow. The effect is surprisingly large. A correction term is derived to compensate for the effect of increased pressure. By reanalysing the results for argon-nitrogen reported in Paper I it is shown that instead of two different isotherms being obtained by making the perturbation with the addition of argon or nitrogen, a single isotherm for each component is obtained.